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Geometrization conjecture
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==References== *L. Bessieres, G. Besson, M. Boileau, S. Maillot, J. Porti, 'Geometrisation of 3-manifolds', EMS Tracts in Mathematics, volume 13. European Mathematical Society, Zurich, 2010. [https://www-fourier.ujf-grenoble.fr/~besson/book.pdf] *M. Boileau [https://web.archive.org/web/20110930020447/http://www.crm.es/Publications/Quaderns/Quadern25-1.pdf Geometrization of 3-manifolds with symmetries] *F. Bonahon ''Geometric structures on 3-manifolds'' Handbook of Geometric Topology (2002) Elsevier. *{{wikicite|ref={{sfnRef|Cao|Zhu|2006}}|reference={{cite journal|author-link1=Huai-Dong Cao|mr=2233789|zbl=1200.53057|author-link2=Xi-Ping Zhu|last1=Cao|first1=Huai-Dong|last2=Zhu|first2=Xi-Ping|title=A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton–Perelman theory of the Ricci flow|journal=[[Asian Journal of Mathematics]]|volume=10|year=2006|issue=2|pages=165–492|doi-access=free|doi=10.4310/ajm.2006.v10.n2.a2|ref=none}}<br>{{cite journal|last1=Cao|first1=Huai-Dong|last2=Zhou|first2=Detang|author-mask1=–|author-mask2=–|mr=2282358|title=Erratum|journal=[[Asian Journal of Mathematics]]|volume=10|issue=4|pages=663–664|doi-access=free|doi=10.4310/AJM.2006.v10.n4.e2|year=2006}}<br>{{cite arXiv|author-mask1=–|author-mask2=–|author-link2=Xi-Ping Zhu|last1=Cao|first1=Huai-Dong|last2=Zhu|first2=Xi-Ping|title=Hamilton–Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture|eprint=math/0612069|year=2006|ref=none}}}} * Allen Hatcher: [http://pi.math.cornell.edu/~hatcher/3M/3M.pdf ''Notes on Basic 3-Manifold Topology''] 2000 *J. Isenberg, M. Jackson, ''Ricci flow of locally homogeneous geometries on a Riemannian manifold'', J. Diff. Geom. 35 (1992) no. 3 723–741. * {{cite journal|author-link1=Bruce Kleiner|last1=Kleiner|first1=Bruce|last2=Lott|first2=John|title=Notes on Perelman's papers|journal=[[Geometry & Topology]]|volume=12|year=2008|issue=5|pages=2587–2855|mr=2460872|doi=10.2140/gt.2008.12.2587|doi-access=free|others=Updated for corrections in 2011 & 2013|zbl=1204.53033|author-link2=John Lott (mathematician)|arxiv=math/0605667}} * [[John Morgan (mathematician)|John W. Morgan]]. [https://www.ams.org/bull/2005-42-01/S0273-0979-04-01045-6/S0273-0979-04-01045-6.pdf ''Recent progress on the Poincaré conjecture and the classification of 3-manifolds.''] Bulletin Amer. Math. Soc. 42 (2005) no. 1, 57–78 (expository article explains the eight geometries and geometrization conjecture briefly, and gives an outline of Perelman's proof of the Poincaré conjecture) *{{Cite book | title = Ricci Flow and Geometrization of 3-Manifolds | year = 2010 | series = University Lecture Series | url = https://www.ams.org/bookstore-getitem/item=ulect-53 | last1 = Morgan | first1 = John W. | last2 = Fong | first2 = Frederick Tsz-Ho | isbn = 978-0-8218-4963-7 | access-date = 2010-09-26 }} * {{cite book|author-link1=John Morgan (mathematician)|last1=Morgan|first1=John|last2=Tian|first2=Gang|title=The geometrization conjecture|series=[[Clay Mathematics Monographs]]|volume=5|publisher=[[Clay Mathematics Institute]]|location=Cambridge, MA|year=2014|isbn=978-0-8218-5201-9|mr=3186136|author-link2=Tian Gang}} * {{cite arXiv|last1=Perelman|first1=Grisha|author-link1=Grigori Perelman|title=The entropy formula for the Ricci flow and its geometric applications|eprint=math/0211159|year=2002}} * {{cite arXiv|last1=Perelman|first1=Grisha|author-link1=Grigori Perelman|title=Ricci flow with surgery on three-manifolds|eprint=math/0303109|year=2003}} * {{cite arXiv|last1=Perelman|first1=Grisha|author-link1=Grigori Perelman|title=Finite extinction time for the solutions to the Ricci flow on certain three-manifolds|eprint=math/0307245|year=2003}} *[[G. Peter Scott|Scott, Peter]] [http://www.math.lsa.umich.edu/~pscott/8geoms.pdf ''The geometries of 3-manifolds.''] ([http://www.math.lsa.umich.edu/~pscott/errata8geoms.pdf errata]) Bull. London Math. Soc. 15 (1983), no. 5, 401–487. *{{Cite journal | last1=Thurston | first1=William P. | author1-link=William Thurston | title=Three-dimensional manifolds, Kleinian groups and hyperbolic geometry | doi=10.1090/S0273-0979-1982-15003-0 | mr=648524 | year=1982 | journal=Bulletin of the American Mathematical Society |series=New Series | issn=0002-9904 | volume=6 | issue=3 | pages=357–381 | doi-access=free }} This gives the original statement of the conjecture. * William Thurston. ''Three-dimensional geometry and topology. Vol. 1''. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, NJ, 1997. x+311 pp. {{ISBN|0-691-08304-5}} (in depth explanation of the eight geometries and the proof that there are only eight) * William Thurston. [http://www.msri.org/publications/books/gt3m/ The Geometry and Topology of Three-Manifolds], 1980 Princeton lecture notes on geometric structures on 3-manifolds.
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